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LECTURE 5: PHASE EQUILIBRIA. PHASE EQUILIBRIA. Phase equilibrium describes the way phases (such as solid, liquid and/or gas) co-exist at some temperatures and pressure, but interchange at others. Energetic introduction to phase equilibria. Why does an ice cube melt in the mouth?.

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slide2

PHASE EQUILIBRIA

Phase equilibrium describes the way phases (such as solid, liquid and/or gas) co-exist at some temperatures and pressure, but interchange at others.

slide3

Energetic introduction to phase equilibria

Why does an ice cube melt in the mouth?

slide4

Further thermodynamic background: terminology

A phaseis a component

within a system,

existing in a precisely

defined physical state,

e.g. gas, liquid, or a

solid that has a single

crystallographic form.

Concerning transitions between the two phases ‘1’ and ‘2’, Hess’s Law states that H(1→2) = −1 ×

H(2→1).

slide6

PHASE TERMINOLOGY

A phase diagram is a graph showing values of applied pressure and temperature at which equilibrium exists.

A phase boundary is a line on a phase diagram representing values of applied pressure and temperature at which equilibrium exists.

The triple point on a phase diagram represents the value of

pressure and temperature at which three phases coexist at equilibrium.

slide8

SPONTANEITY OF PHASE CHANGES

Why does water placed in the freezer become ice?

slide9

SOLID PHASE TRANSITIONS

the tin allotropes have very

different densities ρ, so ρ(tin, grey) = 5.8 gcm−3 but ρ(tin, white) = 7.3 gcm−3.

slide10

KINETICS OF PHASE CHANGES

Phase transitions involving liquids and gases are generally fast!

slide11

Pressure and temperature changes with a single-component system:

How is the ‘Smoke’ in horror films made?

The effect of temperature on phase change: sublimation

slide12

The Effect of Pressure on Phase Change:

How does freeze drying work?

Freeze-drying is a layman’s description, and acknowledges that external conditions may alter the conditions of a phase change, i.e. the drying process (removal of water) occurs at a

temperature lower than 100 ◦C.

slide15

THERMODYNAMICS OF PHASE CHANGES

HOW DOES A ROTARY EVAPORATOR WORKS?

slide16

CRITICAL AND SUPERCRITICAL FLUIDS

How is coffee decaffeinated?

slide17

COFFEE DECAFFEINATED

The intensive properties

of the liquid

and gas (density, heat

capacity, etc.) become

equal at the critical

point, which is

the highest temperature

and pressure at

which both the liquid

and gaseous phases

of a given compound

can coexist.

slide20

QUANTITATIVE ASPECTS OF P-T CHANGE

Why is ice so slippery?

The effect of p and T on the position of solid liquid equilibrium

slide23

SAMPLE PROBLEM:

Consider a car weighing 1000 kg (about 2200 lbs) parked on a sheet of ice at 273.15 K. Take the area under wheels in contact with the ice as 100 cm2 i.e. 10−2 m2. What is the new melting temperature of the ice – call it T(final)? Take H O(melt) = 6.0 kJmol−1 and water Vm(melt) = −1.6 × 10−6 m3 mol−1.

slide24

SAMPLE PROBLEM

Paraffin wax has a normal melting temperature

T(melt) of 320 K. The temperature of equilibrium is raised

by 1.2 K if the pressure is increased fivefold. Calculate Vm for the wax as

it melts. Take H(melt) = 8.064 kJ mol−1.

slide26

PHASE DIAGRAMS

  • knowledge of the thermodynamics of simple mixtures to discuss the physical changes of mixtures when they are heated or cooled and when their compositions are changed.
  • phase diagrams can be used to judge whether two substances are mutually miscible.
slide27

PHASE DIAGRAMS

  • can equilibrium exist over a range of conditions or whether a system must be bought to a definite pressure, temperature and composition before equilibrium is established.
  • phase diagrams are industrially and commercially important.
slide28

PHASE DIAGRAMS

  • semiconductor, ceramics, steel and alloy industries rely heavily on phase diagrams to ensure uniformity of a product.
  • phase diagrams are also the basis for separation procedures in the petroleum industry and the formulation of foods and cosmetic preparations.
slide29

DEFINITIONS

  • A phase is a state of matter that is uniform throughout, not only in composition but also in physical state.
  • A pure gas
  • A gaseous mixture
  • Two totally miscible liquids
  • A crystal
slide30

DEFINITIONS

  • A solution of sodium chloride
  • Ice
  • A slurry of ice and water
slide31

DEFINITIONS

  • An alloy of two metals?
slide33

DEFINITIONS

  • an alloy of two metals is a two phase system if the metals are immiscible, but a single phase system if they are miscible.
  • dispersion can be uniform on a macroscopic level, but not on a microscopic scale.
  • dispersions are important in many advanced materials.
slide34

DEFINITIONS

  • heat treatment cycles are used to achieve the precipitation of a fine dispersion of particles of one phase within a matrix formed by a saturated solid solution phase.
  • the ability to control this microstructure resulting from phase equilibria makes it possible to tailor the mechanical properties of the materials.
slide35

DEFINITIONS

  • A constituent of a system is a chemical species (an ion or a molecule) that is present.
  • A mixture of water and ethanol has two constituents.
  • A solution of sodium chloride has three constituents: Na+, Cl-, H2O.
slide36

DEFINITIONS

  • acomponent is a chemically independent constituent of a system.
  • the number of components in a system is the minimum number of independent species necessary to define the composition of all the phases present in the system.
slide37

DEFINITIONS

  • When no reaction takes place and there are no other constraints, the number of components is the equal to the number of constituents.
  • Pure water is a one component system
  • A mixture of ethanol and water is two component system.
slide38

DEFINITIONS

  • an aqueous solution of sodium chloride is a two component system, because by charge balance, the number of Na+ ions must be the same as the number of Cl- ions.
  • a system that consists of hydrogen, oxygen and water at room temperature has three components.
slide39

DEFINITIONS

  • when a reaction can occur under the conditions prevailing in the system, we need to decide the minimum number of species that, after allowing for reactions in which one species is synthesized from others, can be used to specify the composition of all the phases.
slide40

DEFINITIONS

  • CaCO3(s) CaO(s) + CO2(g)
  • 3 phases
  • 3 constituents
  • To specify the composition of the gas phase, we need the species CO2, and to specify the composition of the solid phase on the right, we need the species CaO.
slide41

DEFINITIONS

  • CaCO3(s) CaO(s) + CO2(g)
  • We do not need an additional species to specify the composition of the phase on the right, because its identity (CaCO3) can be expressed in terms of the other two constituents by making use of the stoichiometry of the reaction.
  • 2 component system.
sample problem
SAMPLE PROBLEM

How many components are present in a system in which ammonium chloride undergoes thermal decomposition?

The reaction is:

NH4Cl(s)  NH3(g) + HCl(g)

slide43

DEFINITIONS

  • NH4Cl(s) NH3(g) + HCl(g)
  • 2 phases
  • 3 constituents
  • 1 component
sample problem1
SAMPLE PROBLEM
  • Give the number of components in the following systems: (a) water, allowing for its autoprotolysis, (b) aqueous acetic acid, (c) magnesium carbonate in equilibrium with its decomposition products.
slide45

DEFINITIONS

  • The number of phases, P.
  • The number of components, C.
  • The variance of the system, F is the number of intensive variables (e.g. p and T) that can be changed independently without disturbing the number of phases in equilibrium.
slide46

PHASE RULE

  • F = C – P + 2
  • This is not an empirical rule based upon observations, it can be derived from chemical thermodynamics
  • For a one component system F = 3 – P
  • When only one phase is present, F = 2 and both p and T can be varied without changing the number of phases.
slide47

PHASE RULE

  • When two phases are present, F = 1 which implies that pressure is not freely variable if the pressure is set. This is why at a given temperature a liquid has a characteristic vapor pressure.
  • When three phases are present, F = 0. This special case occurs only at a definite temperature and pressure that is characteristic of the substance.
slide49

EXPERIMENTAL PROCEDURE

  • Thermal analysis – a sample is allowed to cool and it temperature is monitored. When a phase transition occurs, cooling may stop until the phase transition is complete and is easily observed on a thermogram.
slide51

EXPERIMENTAL PROCEDURES

  • Modern work on phase transitions often deal with systems at very high pressures and more sophisticated detection properties must be adopted.
  • A diamond anvil cell is capable of producing extremely high pressures.
slide52

PHASE RULE

  • a sample is placed in a cavity between two gem-quality diamonds and then pressure is exerted by turning a screw. Pressures up to ~2 Mbar can be achieved.
  • one application is the study the transition of covalent solids to metallic solids.
slide54

EXPEIMENTAL PROCEDURES

  • Iodine, I2, becomes metallic at ~ 200 kbar and makes a transition to a monatomic metallic solid at around 210 kbar.
  • Relevant to the structure of material deep inside the earth and in the interiors of giant planets, where even hydrogen may be metallic.
slide55

TWO COMPONENT SYSTEM

  • When two components are present in a system,

C = 2, so F = 4 – P.

  • If the temperature is constant, the remaining variance is F’ = 3 – P.
  • F’ indicates that one of the degrees of freedom has been discarded – in this case the temperature.
  • The two remaining degrees of freedom are the pressure and the composition
slide56

TWO COMPONENT SYSTEM

  • The partial vapor pressure of the components of an ideal solution of two volatile liquids are related to the composition of the liquid mixture by Raoult’s Law:
slide57

TWO COMPONENT SYSTEM

  • This expression shows that the total vapor pressure (at a fixed temperature) changes linearly with the composition from pB* to pA* as xA changes from 0 to 1.
slide59

TWO COMPONENT SYSTEM

  • The compositions of the liquid vapor that are in mutual equilibrium are not necessarily the same. The more volatile the component, the higher amount of that substance should be in the vapor.
  • yA and yB are the mole fractions of A and B in the gas.
slide63

TWO COMPONENT SYSTEM

  • If we are interested in distillation, both vapor and liquid compositions are of equal interest.
  • So it makes sense to present data showing both the dependence of vapor and liquid composition upon mole fraction.
slide67

LEVER RULE

  • A point in the two-phase of a phase diagram indicates not only qualitatively that both liquid and vapor present, but represents quantitatively the relative amounts of each.
  • To find the relative amounts of two phases a and b that are in equilibrium, we measure the distances la and lb along the horizontal tie line, and then use the lever rule.
slide69

LEVER RULE

  • Where na is the amount of phase a and nb is the amount of phase b.
slide70

TEMPERATURE COMPOSITION DIAGRAMS

  • To discuss distillation we need a temperature-composition diagram instead of a pressure-composition diagram.
  • Such a diagram shows composition at different temperatures at a constant pressure (typically 1 atm).
slide72

TEMPERATURE COMPOSITION DIAGRAMS

  • In a simple distillation the vapor is withdrawn and condensed. This technique is used to separate a volatile liquid from a non-volatile solute or solid.
  • In a fractional distillation, the boiling and condensation cycle is repeated successively. This technique is used to separate volatile liquids.
slide73

TEMPERATURE COMPOSITION DIAGRAMS

  • The efficiency of a fractionating column is expressed in terms of the number of theoretical plates, the number of effective vaporization and condensation steps that are required to achieve a condensate of given composition from a given distillate.
slide75

AZEOTROPES

  • Although many liquids have temperature-composition phase diagrams resembling the ideal version, a number of important liquids deviate from ideality.
  • If a maximum occurs in the phase diagram, favorable interactions between A and B molecules stabilize the liquid.
slide78

AZEOTROPES

  • An azeotrope is a mixture of two (or more) miscible liquids that when boiled produce the same composition in the vapor phase as that is present in the original mixture.
slide79

LIQUID-LIQUID PHASE DIAGRAMS

  • Let’s consider the distillation of two immiscible liquids, such as octane and water.
  • The system can be considered as the joint distillation of the separated components.
  • Total vapor pressure p = pA* + pB*
  • Mixture boils when p = 1 atm, and so the mixture boils at a lower temperature than either component would alone.
slide81

LIQUID-LIQUID PHASE DIAGRAMS

  • Let’s consider temperature-composition diagrams for systems that consist of pairs of partially miscible liquids.
  • Partially miscible liquids are liquids that do not mix at all proportions at all temperatures.
slide82

PHASE SEPARATION

  • Suppose a small amount of liquids B is added to another liquid A at a temperature T’.
  • If it dissolves completely the binary mixture is a single phase.
  • As more B is added, A becomes saturated in B and no more B dissolves  2 phases.
  • Most abundant phase is A saturated with B.
  • Minor phase is B saturated with A.
phase separation
PHASE SEPARATION
  • The relative abundance of each phase is given by the lever rule.
  • As the amount of B increases the composition of each phase stays the same, but the amount of each changes with the lever rule.
  • Eventually a point is reached when so much B is present that it can dissolve all the A, and system reverts to a single phase.
sample problem2
SAMPLE PROBLEM

A mixture of 50 g of hexane (0.59 mol C6H14) and 50 g of nitrobenzene (0.41 molC6H5NO2) was prepared at 290 K. What are the compositions of the phases, and in what proportions do they occur? To what temperature must the sample be heated in order to obtain a single phase?

critical solution temperatures
CRITICAL SOLUTION TEMPERATURES
  • The upper critical solution temperature, Tuc is the highest temperature at which phase separation occurs.
  • Above the critical temperature the two components are fully miscible.
  • On the molecular level, this can be interpreted as the kinetic energy of each molecule over coming molecular interactions that want molecules of one type to come close together.
critical solution temperatures1
Critical solution temperatures
  • Some systems show a lower critical solution temperature, Tlc.
  • Below this temperature the two components mix in all proportions and above which they form two phases.
  • An example is water and triethylamine.
critical solution temperatures2
CRITICAL SOLUTION TEMPERATURES
  • The molecular reason for this is that water and triethylamine form a weak molecular complex. At higher temperatures the complexes break up and the two components are less miscible.
  • Some systems have upper and lower critical solution temperatures.
distillation of partially miscible liquids
DISTILLATION OF PARTIALLY MISCIBLE LIQUIDS
  • What happens when you distill partially miscible liquids?
  • A pair of liquids that are partially miscible often form a low-boiling azeotrope.
  • Two possibilities can exist: one in which the liquid become fully miscible before they boil; the other in which boiling occurs before mixing is complete.
liquid solid phase diagrams
LIQUID-SOLID PHASE DIAGRAMS
  • The knowledge of temperature-composition diagrams for solid mixtures guides the design of important industrial processes, such as the manufacture of liquid crystal displays and semiconductors.
eutectics
EUTECTICS
  • The isopleth at e corresponds to the eutectic composition, the mixture with the lowest melting point.
  • A liquid with a eutectic composition freezes at a single temperature without depositing solid A or B.
  • A solid with the eutectic composition melts without any change of composition at the lowest temperature of any mixture.
eutectics1
EUTECTICS
  • Solder – 67% tin and 33% lead by mass melts at 183 °C.
  • 23% NaCl and 77% H2O by mass forms a eutectic mixture which melts at -21.1 °C. Above this temperature the mixture melts.
reacting systems
REACTING SYSTEMS
  • Many binary mixtures react produce compounds.
  • Gallium arsenide is a technologically important example – semiconductor.
  • Ga + As  GaAs